Relationship between mechanical advantage, velocity ratio, and efficiency – state & derive

Last updated on June 26th, 2023 at 02:04 pm

In this post, we will first state the Relationship between mechanical advantage, velocity ratio, and efficiency. Then we will derive the relationship between mechanical advantage, velocity ratio, and efficiency of a machine.

State the Relationship between mechanical advantage, velocity ratio, and efficiency | formula, equation

Efficiency = Mechanical Advantage/Velocity Ratio

η = M.A. / V.R.

M.A. = η x V.R.

[Here, η = efficiency, M.A. = Mechanical Advantage, and V.R. = Velocity Ratio]

Derive the Relationship between mechanical advantage, velocity ratio, and efficiency | derivation

The efficiency of a machine (η) = Work output / Work input …. (1)
Now, Work output = Load x displacement of the load ….. (2)
And Work Input = Effort X displacement of the effort ….. (3)

From all 3 equations above,
Efficiency (η) = Work output / Work input
=> η = Work output / Work input
=> η = (Load x displacement of the load)/(Effort X displacement of the effort)
=> η = (Load/Effort) x (displacement of load/displacement of effort)
=> η = Mechanical Advantage x (1/Velocity Ratio)
η = Mechanical Advantage/Velocity Ratio

Efficiency= Mechanical Advantage/Velocity Ratio
η = MA/VR

Mechanical Advantage equals Velocity Ratio for an ideal machine – How?

For an ideal machine, Work output = Work input
and hence for an ideal machine efficiency η = 1 or 100%
So, for an ideal machine, η = 1
As we know, η = MA/VR
So, in this case of an ideal machine, 1 = MA/VR
so, Hence, for an ideal machine MA = VR